We describe an experiment in which a train of femtosecond pulses is coupled into a photonic crystal fiber (PCF) by means of an offset pumping technique that can selectively excite either the mode LP01 or LP11 or LP21. The PCF presents a wide range of wavelengths in which the fundamental mode experiences normal dispersion, whereas LP11 and LP21 propagate in the anomalous dispersion regime, generating a supercontinuum based on the soliton fission mechanism. We find that the existence of a cut-off wavelength for the higher-order modes makes the spectral broadening asymmetrical. This latter effect is particularly dramatic in the case of the LP21 mode, in which, by using a pump wavelength slightly below cut-off, the spectral broadening occurs only on the blue side of the pump wavelength. Our experimental results are successfully compared to numerical solutions of the nonlinear Schrödinger equation.